You might be getting into trouble by visualizing a capacitor as being like two separate plates. Are you assuming that you can remove 1uC of charge from one plate, but not removing any charge from the other? That may be OK for physics homework (where capacitors are two metal spheres at great distance.) But in electronics, capacitors are relatively huge plates, spaced microscopically apart. An electrical engineer's capacitor isn't like two separate metal spheres. Instead it behaves like a single ball with a microscopic gap sliced all the way through it. Two solid polished hemispheres separated by a micron of plastic film.
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/ || \ "Engineer's Capacitor"
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| || | A spilt metal sphere with
| || | a very narrow gap between
| || | the two halves
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In other words, the capacitance to distant ground is tiny, while capacitance between the two hemispheres is enormous. The main effect is that, if you try to force some charge continuously into one plate of this "engineer's capacitor," that charge instantly spreads to the outer surface of both plates. And then, a large voltage appears on both plates WRT ground, halting the current. The only way to avoid this effect, and to create a continuing current, is by treating the capacitor as a two-terminal conductor. In that case we cannot push charge into the first plate unless simultaneously we remove it from the second.
The capacitor only works right if we pretend that it's some sort of wire. With wires, if we try to push in more charge than we remove, both ends of the wire immediately charge up to fantastic values of voltage, and this blocks any further current. A capacitor in electronics does the same thing. More: the engineer's capacitor
Why does this occur? I personally find this fascinating. If we dump positive charge into one hemisphere, it spreads out over the surface, including that part of the surface down in the gap between hemispheres. The positive charge that went into the gap attracts equal negative charge to the other side of the gap. But this leaves a positive excess in the second hemisphere, and this excess self-repels, traveling to the outer surface of the second hemisphere. If the surface excess on the second half grows too large, then the opposite happens, and excess negative in the gap will create excess negative on the outside of the original hemisphere. When things have settled down, half the charge that we placed on one hemisphere has seemingly traveled to the outer surface of the second hemisphere! And, down in the gap, each flat face also has half the amount of deposited charge, but on the second hemisphere it's opposite polarity.
So, capacitors act like single metal objects, where charge seemingly leaps the gap with ease. Electrically, the two halves are coupled together very, very tightly. To produce a current, we're required to connect them in a circuit, where the path for current is through the component, and back out again. And then of course the capacitor equation takes hold ...for every second the current through the capacitor exists, the voltage between the plates grows in proportion to I/C, and energy is stored in the gap. A capacitor is a 2-terminal component, and not anything like an open circuit or a pair of widely-spaced plates. The path for current is through.